The Dresden Maya Codex


The Dresden Maya Codex from about 1200 to 1250 is one of the very few written documents of the pre-Columbian Maya culture that have survived to the present day. It contains 3 astronomical tables:

The Maya calendric system consits of:

  • the Haab, a 365-day calendar approximating the solar year, having 18 months of 20 days and
    one month of 5 days;
    see my JavaScript.

  • the Tzolkin, a 260-day calendar, with 20 periods of 13 days, used in the society, in rituals,
    and in religious and ceremonial events.
    see my applet or JavaScript.

  • a Long Count date is specified by the number of days from a starting date (August 11, 3114 BCE in Gregorian calendar), using a base-20 and base-18 number system, consisting of 5 fields:
    • baktun = 144,000 days
    • katun = 7,200 days
    • tun = 360 days
    • winal = 20 days
    • kin = 1 day
    The starting date is written 0.0.0.0.0, the maximum date is 19.19.19.17.19, the Gregorian date 4772 October 12.

A Calendar Round is a combination of the Haab and the Tzolkin. The total number of combinations is

365 Haab days x 260 Tzolkin days = 94,900 days.

But the two calendars repeat after 52 Haab years of 365 days, because of the same number of days as in 73 Tzolkin years of 260 days:

52 · 365 = 73 · 260 = 18,980 = 94,900 : 5

Not every possible combination of Tzolkin and Haab can occur, only 1 in 5 combinations are possible.
E. g. for Tzolkin days Ajaw the Haab day can only be 3, 8, 13 or 18. To show this set the Haab calculator to 8 Kumku (the date of creation, which is 4 Ajaw in Tolkin). Then add a multiple of 20 (e.g. 380 to jump into the next cycle) leaving Ajaw unchanged.


Venus Tables

Venus motion details

Heliacal Rise of Venus

Venus was of utmost importance for the Mayas, considered to bring evil and misfortune when appearing in the morning sky.
Page (24) of the Codex at the left is an introduction to the Venus tables, listing the multiples of 2920, the period of the Venus cycle, beginning in the low right corner:


Venus Table Maya 1920
http://www.mexicolore.co.uk/images-ans/ans_38_01_2.jpg

The base of the Mayan number System is 20, using 18·20=360 in the 3rd to the last digit and 20·360=7200 in the 4th to the last digit:

Maya Codex Venus tables page
                  24

The blue frame:

5 · 2920 = 14600 = 2·7200 + 10·20 = 2.0.10.0

6 · 2920 = 17520 = 2·7200 + 8·360 + 12·20 = 2.8.12.0

7 · 2920 = 20440 = 2·7200 + 16·360 + 14·20 = 2.16.14.0

8 · 2920 = 23360 = 3·7200 + 4·360 + 16·20 = 3.4.16.0

The green frame:

9 · 2920 = 26280 = 3·7200 + 13·20 = 3.13.0.0

10 · 2920 = 29200 = 4·7200 + 1·360 + 2·20 = 4.1.2.0

11 · 2920 = 32120 = 4·7200 + 9·360 + 4·20 = 4.9.4.0

12 · 2920 = 35040 = 4·7200 + 17·360 + 6·20 = 4.17.6.0

The black frame:

13 · 2920 = 37960 = 5·7200 + 5·360 + 8·20 = 5.5.8.0

26 · 2920 = 75920 = 10·7200 + 10·360 + 16·20 = 10.10.16.0

39 · 2920 = 113880 = 15·7200 + 16·360 + 6·20 = 15.16.6.0

52 · 2920 = 151840 = 1·144000 + 1·7200 + 1·360 + 14·20 = 1.1.1.14.0


Between the black and the green frame there are correction numbers, because the exact synodic period of Venus is not 584 days but 593,92 days: a shift of 1 day in 13 cycles.

Page 24 is followed by Venus tables on pages 46 to 50, showing certain dates within the 584 days of Venus cycle. On the left of page 46 we find the numbers (orange frame from left to right):

11.16 = 11·20 + 16 = 236

16.6 = 16·20 + 6 = 326,  326 - 236 = 90

1.10.16 = 1·360 + 10·20 + 16· = 576,  576 - 326 = 250

1.11.4 = 1·360 + 11·20 + 4· = 584,  584 - 576 = 8

The table starts on the date when Venus vanishes from the morning sky (invisible at upper conjunction, 236 in the first column on the left).
90 days later Venus becomes visible in the evening sky (326, second column).
This period lasts for 250 days, until Venus enters the lower conjunction, being invisible for 8 days. Thereafter the planet reappears as the Morning star in the east.
The sum is:
236 + 90 + 250 + 8 = 584.


The dashed red frame on page 46 consists of 4 columns:
 A.  dates when Venus vanishes from the morning sky (invisible for 90 days),
 B.  90 days later, when Venus appears in the evening sky (visible for 250 days),
 C.  250 days later, when Venus vanishes from the evening sky, (invisible for 8 days),
 D.  8 days later, when Venus appears in the morning sky (visible for 236 days).

In the first line we find the numbers:
venus table page 46
                        line 1

3, followed by 2 = (3 + 90) mod 13, followed by 5 = (2+250) mod 13, and 13 = 5 + 8.

The second line (cell A2) starts using the last number of the preceeding line (D1):
11 = (13 + 260 - 236) mod 13= (13 + 24) mod 13 = 11.

The complete table can be computed this way (if result = number mod 13 = 0 then result = 1).


Venus Tabelle page 46

The intervals 90, 250, 8, 236 used in the Tzolkin are only rough approximations to the true periods: 90 days of invisibilty around upper conjunction is far too long, it is only about 50 days (*).
The periods as evening and morning star each average about 263 days. So we have:
263 + 50 + 263 + 8 = 584 (**)

Venus conjunction

Neglecting the small eccentricities of the Earth (0.0161) and of Venus (0.0068) my applet "Geocentric Motion" is computing the elongation angle between Venus and the Sun:

Venus elongation
                          angle of the Sun

Venus elongation angle daily change

The mean daily change of the elongation angle is about 1.63° per day around inferior conjunction, and the elongation changes from -6,6° to 6.6° within 8 days.
Around superior conjunction (0,162° per day) the elongation takes about 50 days to change from -6.6° to 6.5° degrees.




Books
Grube, Nikolai: Der desdner Maya-Kalender. Der vollständige Codex; Herder, Freiburg 2012; ISBN 978-3-451-33332-3

Grube, Nikolai (Hg.): Maya, Gottkönige im Regenwald; h.f. ullmann, Potsdam 2012; ISBN 978-3-8480-0033-3
Links

Heliacal rising (Wikipedia)

Show Me a Dawn, or "Heliacal," Rising (QuickTime required)

Introducing the Venus Cycle

Planetary Phenomena of Venus from 2000 through 2100 (Astrodienst)

The "Arcus Visionis" of the Planets in the Babylonian Observations (C. Schoch)

The Dresden Maya Codex (SLUB)

Dresden Codex (Wikipedia)

(*)  Maya Astronomy: Venus

(**) The Evening and Morning Star

Maya Observations of very long periods of Venus

The Dresden Codex (Andreas Fuls)

Bricker, Harvey, and Victoria R. Bricker (1983) Classic Maya Prediction of Solar Eclipses. Current Anthropology. Vol. 24, pp. 1-23.

The Dresden Codex - Eclipse Tables (M. J. Finley)

Five millennium catalog of solar eclipses (NASA, Fred Espenak)

Lunar node (Wikipedia)

PlanetObserver Applet

To the Limits (David Dearborn)

Mayan Calendar Description (Stephen P. Morse)

Mayan Calendar Conversions in One Step (Stephen P. Morse)

Ancient Maya documents concerning the movements of Mars




Updated: 2015, Feb 14